Is this allowed in 8th? p. 43 of the BRB says you can't go below 1, but on p.179 you can reduce an opponent's armor by -7 (which would suggest you can go to at least 0+). Any insight?
Yes and no. You can build a model with 0+ AS but for virtually all rules purposes he will act as having 1+. The only exception is when some magic or special rule reduces the AS of his armour he will have 1+ AS when other models will be dropping to 2+. Note that for all game purposes 0+ doesn't exist, it just means that the first point of AS eliminated from the model doesn't reduce the 1+ save as the model had a spare point of unused armour that is no longer spare.
Actually, the 3rd paragraph of page 43 specifically says you can't make a model with better than 1+. It's not simply talking about a 1 always failing (though it does also state that), it's saying you can't make 0+, negative 1+ etc. I would assume that the table on the same page showing 9 and 10 strength reducing the save by 6 and 7 is an oversight. In the FAQ, it talks about not preventing models from taking items that would take the armour save lower. This means that if you've got a 1+ armour save, you can still take that light armour, but it won't make it 0+. So, in the situation you're character has equipment that would give him 0+, his save is still only 1+. If he takes a Str 5 hit, his save is at 3+; the extra armour does not suddenly "kick-in" to give a 2+ save. tl;dr: No.
BEEGfrog might be referring to spells that permanently destroy armour or magic items. HE have Vaul's Unmaking, I think lore of metal might have something as well. They usually just revert back to the mundane version anyway so it still would rarely make a difference.
There is still technically one set up in the game that can reach a 0+ armour save - Warriors of Chaos. On the eye of the gods table, one of the rolls increases the AS by 1 to a max of 0+ so a 1+ character or unit of knights could do it if they get the +1 AS roll on the table. Since the book specifically states they can reach 0+, this supersedes the CRB. They still fail on a 1 though so a WoC player will generally try to get a new roll ASAP.